提出用一组共识排序替代单一排序，更好解释输入偏好。
A consensus set for the aggregation of partial rankings: the case of the Optimal Set of Bucket Orders Problem
- 用多个共识排序替代单一排序，捕捉输入数据的多样性
- 在OBOP基础上扩展出OSBOP，显著提升解的适应度
- 适合需要解释多样偏好或复杂排序的场景
在排名聚合问题（RAP）中，通常以一个共识排序作为解来概括输入的多个排序。不同变体在输入输出类型及目标函数上存在差异。然而，在某些机器学习或多元优化任务中，需关注输入数据或搜索空间中的多样性，因此本文提出：将排名聚合的解从单一共识排序改为一组共识排序，以更全面地解释输入偏好。通过最优分桶序问题（OBOP）为例，该问题旨在从优先级矩阵编码的输入排序中找出一个带并列的共识排序。为此，本文引入最优分桶序集合问题（OSBOP），即推广原问题，目标是生成一组共识排序而非单一排序。实验表明，通过提供一组共识排序，解的适应度显著优于原始OBOP，且保持可解释性。
原文摘要 · Abstract (English)
In rank aggregation problems (RAP), the solution is usually a consensus ranking that generalizes a set of input orderings. There are different variants that differ not only in terms of the type of rankings that are used as input and output, but also in terms of the objective function employed to evaluate the quality of the desired output ranking. In contrast, in some machine learning tasks (e.g. subgroup discovery) or multimodal optimization tasks, attention is devoted to obtaining several models/results to account for the diversity in the input data or across the search landscape. Thus, in this paper we propose to provide, as the solution to an RAP, a set of rankings to better explain the preferences expressed in the input orderings. We exemplify our proposal through the Optimal Bucket Order Problem (OBOP), an RAP which consists in finding a single consensus ranking (with ties) that generalizes a set of input rankings codified as a precedence matrix. To address this, we introduce the Optimal Set of Bucket Orders Problem (OSBOP), a generalization of the OBOP that aims to produce not a single ranking as output but a set of consensus rankings. Experimental results are presented to illustrate this proposal, showing how, by providing a set of consensus rankings, the fitness of the solution significantly improves with respect to the one of the original OBOP, without losing comprehensibility.
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